We study convergence rates of Bayesian density estimators based on finite location-scale mixtures of exponential power distributions. We construct approximations of β-Hölder densities be continuous mixtures of exponential power distributions, leading to approximations of the β-Hölder densities by finite mixtures. These results are then used to derive posterior concentration rates, with priors based on these mixture models. The rates are minimax (up to a logn term) and since the priors are independent of the smoothness the rates are adaptive to the smoothness.
Kruijer, W. T., Rousseau, J., & van der Vaart, A. (2010). Adaptive Bayesian density estimation with location-scale mixtures. Electronic Journal of Statistics, 4, 1225-1257. https://doi.org/10.1214/10-EJS584